Question
At what temperature will the oxygen molecules have the same root mean square speed as hydrogen molecules at $200 \,K$ ....... $K$
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Answer
${v_{rms}} = \sqrt {\frac{{3RT}}{M}} \Rightarrow \,\,T \propto M$ [Since ${v_{rms}},\,\,R \to $ constant ]
$ \Rightarrow \,\,\,\frac{{{T_{{O_2}}}}}{{{T_{{H_2}}}}} = \frac{{{M_{{O_2}}}}}{{{M_{{H_2}}}}} \Rightarrow \,\,\frac{{{T_{{O_2}}}}}{{200}} = \frac{{32}}{2}\, \Rightarrow \,\,{T_{{O_2}}} = 3200\,K$
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